{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "e80ecac5",
   "metadata": {},
   "source": [
    "![](http://cdn.sealight.site/notes/202510151224938.png)\n",
    "\n",
    "答案选择 A ; train_test_split 的使用方法如下"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "4520db7f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "原始特征数据形状: (150, 4)\n",
      "训练集特征形状: (112, 4)\n",
      "测试集特征形状: (38, 4)\n",
      "训练集标签形状: (112,)\n",
      "测试集标签形状: (38,)\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.datasets import load_iris\n",
    "import numpy as np\n",
    "\n",
    "# 1. 准备数据\n",
    "# 以鸢尾花数据集为例\n",
    "iris = load_iris()\n",
    "X = iris.data  # 特征数据\n",
    "y = iris.target # 标签数据\n",
    "\n",
    "# 2. 分割数据\n",
    "# 默认情况下，75%的数据用于训练，25%的数据用于测试\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.25, random_state=42)\n",
    "\n",
    "print(f\"原始特征数据形状: {X.shape}\")\n",
    "print(f\"训练集特征形状: {X_train.shape}\")\n",
    "print(f\"测试集特征形状: {X_test.shape}\")\n",
    "print(f\"训练集标签形状: {y_train.shape}\")\n",
    "print(f\"测试集标签形状: {y_test.shape}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6079919e",
   "metadata": {},
   "source": [
    "![](http://cdn.sealight.site/notes/202510151235925.png)\n",
    "选B : 训练模型"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "8749860c",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "正在训练模型...\n",
      "模型训练完成！\n",
      "\n",
      "使用训练好的模型进行预测...\n",
      "预测结果 (前5个): [-63.05724905  68.62915855  37.40412291 -19.12809122 -11.71543847]\n",
      "\n",
      "评估模型在测试集上的性能...\n",
      "模型 R² 分数: 0.8094\n"
     ]
    }
   ],
   "source": [
    "from sklearn.model_selection import train_test_split\n",
    "from sklearn.linear_model import LinearRegression\n",
    "from sklearn.datasets import make_regression\n",
    "import numpy as np\n",
    "\n",
    "# 1. 创建示例数据\n",
    "X, y = make_regression(n_samples=100, n_features=1, noise=20, random_state=42)\n",
    "\n",
    "# 2. 划分数据集\n",
    "X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=42)\n",
    "\n",
    "# 3. 创建模型实例\n",
    "model = LinearRegression()\n",
    "\n",
    "# 4. 训练模型 (使用 fit)\n",
    "print(\"正在训练模型...\")\n",
    "model.fit(X_train, y_train)\n",
    "print(\"模型训练完成！\")\n",
    "\n",
    "# 5. 预测新数据 (使用 predict)\n",
    "print(\"\\n使用训练好的模型进行预测...\")\n",
    "y_pred = model.predict(X_test)\n",
    "print(\"预测结果 (前5个):\", y_pred[:5])\n",
    "\n",
    "# 6. 评估模型 (使用 score)\n",
    "print(\"\\n评估模型在测试集上的性能...\")\n",
    "score = model.score(X_test, y_test)\n",
    "print(f\"模型 R² 分数: {score:.4f}\")\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "3776799d",
   "metadata": {},
   "source": [
    "![](http://cdn.sealight.site/notes/202510151239448.png)\n",
    "\n",
    "| 特性 | **标准化** | **归一化** |\n",
    "| :--- | :--- | :--- |\n",
    "| **核心思想** | 均值为0，标准差为1 | 最小值为0，最大值为1 |\n",
    "| **公式** | `(X - mean) / std` | `(X - min) / (max - min)` |\n",
    "| **结果范围** | 无特定范围，理论上可以是任意实数 | 固定在 `[0, 1]` 区间 |\n",
    "| **应用场景** | 适用于数据分布近似高斯分布的情况；对异常值相对不敏感。 | 适用于需要将数据限定在一定范围内的情况（如图像处理）；对异常值非常敏感。 |\n",
    "| **典型算法** | 线性回归、逻辑回归、SVM、PCA、K-Means等。 | KNN、K-Means、图像处理等。 |\n",
    "\n",
    "---\n",
    "\n",
    "正确答案是 C"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "345f50e4",
   "metadata": {},
   "source": [
    "![](http://cdn.sealight.site/notes/202510151246228.png)\n",
    "\n",
    "答案是 D ; C 选项是确定性的线性关系, 无需回归"
   ]
  },
  {
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    }
   },
   "cell_type": "markdown",
   "id": "85a9fa6f",
   "metadata": {},
   "source": [
    "![截图_20251015130757.png](attachment:截图_20251015130757.png)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e502ef0c",
   "metadata": {},
   "source": [
    "![](http://cdn.sealight.site/notes/202510151407296.png)\n",
    "题目问：在线性回归预测信用额度 (credit limit) 的模型中，哪个特征在一个好的假设里应该有 **正权重**（positive weight）。\n",
    "\n",
    "* **A. birth month（出生月份）**\n",
    "  和信用额度没有线性相关关系，1 月和 12 月不会系统性影响信用额度。\n",
    "  → 无意义特征。\n",
    "\n",
    "* **B. monthly income（月收入）**\n",
    "  收入越高，信用额度通常越高。\n",
    "  → **应为正权重**。\n",
    "\n",
    "* **C. current debt（当前负债）**\n",
    "  负债越多，银行会更保守，额度可能降低。\n",
    "  → 负相关，应为负权重。\n",
    "\n",
    "* **D. number of credit cards owned（信用卡数量）**\n",
    "  拥卡多不一定意味着信用额度高，反而可能表示风险高或信用额度已分散。\n",
    "  → 不稳定，但总体不一定正相关。\n",
    "\n",
    "---\n",
    "\n",
    "✅ **正确答案：B. monthly income**\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f5f5cd8c",
   "metadata": {},
   "source": [
    "![](http://cdn.sealight.site/notes/202510151510244.png)\n",
    "简单 ; 假设空间下, 表达能力弱, 容易欠拟合"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "73275978",
   "metadata": {},
   "source": [
    "![](http://cdn.sealight.site/notes/202510151517169.png)\n",
    "\n",
    "# 误差在变量模型\n",
    "\n",
    "简单来说，**误差在变量模型（EIV）** 是一种统计模型，它在标准的回归模型基础上，额外考虑了**自变量（X）也存在测量误差**的情况。\n",
    "\n",
    "---\n",
    "\n",
    "### 1. 为什么需要 EIV 模型？\n",
    "\n",
    "在经典的线性回归模型（比如普通最小二乘法，OLS）中，我们有一个基本假设：所有的自变量（X）都是精确测量的，没有误差，只有因变量（Y）存在随机误差。其模型形式如下：\n",
    "\n",
    "*   **经典回归模型**:  $Y = \\beta_0 + \\beta_1 X + \\epsilon$\n",
    "\n",
    "这个模型假设我们观察到的 `X` 就是真实的 `X`。但在现实世界的许多应用中，这个假设并不成立。例如：\n",
    "\n",
    "*   **经济学**：国民生产总值（GDP）、通货膨胀率等宏观经济数据在统计时本身就有误差。\n",
    "*   **医学**：测量血压、血糖水平时，仪器读数和人为操作都会引入误差。\n",
    "*   **物理学**：在实验中测量位置、速度或温度时，任何测量工具都有其固有的精度限制。\n",
    "\n",
    "当自变量 `X` 存在测量误差时，如果仍然使用经典回归模型，会导致一个严重的问题：**参数估计的有偏性（Bias）**。具体来说，它会系统性地低估自变量 `X` 对因变量 `Y` 的影响，这个现象被称为**衰减偏误（Attenuation Bias）**，即估计出的回归系数 $\\beta_1$ 会趋向于零。\n",
    "\n",
    "### 2. EIV 模型的核心思想\n",
    "\n",
    "EIV 模型通过明确地将自变量的测量误差纳入模型中来解决这个问题。\n",
    "\n",
    "假设我们有：\n",
    "*   $Y_i$：因变量的真实值\n",
    "*   $X_i^*$：自变量的真实但**无法直接观测**的值\n",
    "*   $X_i$：我们实际观测到的自变量值\n",
    "\n",
    "EIV 模型的基本结构如下：\n",
    "\n",
    "1.  **真实关系方程**: $Y_i = \\beta_0 + \\beta_1 X_i^* + \\epsilon_i$\n",
    "    *   这描述了因变量和**真实**自变量之间的线性关系。$\\epsilon_i$ 是因变量的随机误差。\n",
    "\n",
    "2.  **测量误差方程**: $X_i = X_i^* + \\delta_i$\n",
    "    *   这描述了我们观测到的自变量 `X` 是由其真实值 `X*` 和一个测量误差 `δ` 组成的。\n",
    "\n",
    "这里的核心区别在于，模型承认我们用于回归的 `X` 并不是真实的 `X*`，而是带有“噪声”的版本。\n",
    "\n",
    "### 3. EIV 模型的主要类型\n",
    "\n",
    "根据对误差项性质的不同假设，EIV 模型可以分为几类：\n",
    "\n",
    "*   **函数模型 (Functional Model)**: 将真实的自变量 $X_i^*$ 视为未知的、固定的常数。这意味着我们不对 $X_i^*$ 的分布做任何假设，只关心每次测量中的具体值。\n",
    "*   **结构模型 (Structural Model)**: 将真实的自变量 $X_i^*$ 视为随机变量，并假设它服从某个特定的概率分布（例如正态分布）。这种模型在经济学等领域更常见，因为它允许研究变量之间的内在随机关系。\n",
    "\n",
    "### 4. 如何估计 EIV 模型？\n",
    "\n",
    "由于 $X_i^*$ 是不可观测的，我们无法直接使用普通最小二乘法（OLS）来估计 $\\beta_0$ 和 $\\beta_1$。解决这个问题需要引入额外的信息或使用更复杂的估计方法。\n",
    "\n",
    "常见的方法包括：\n",
    "\n",
    "*   **戴明回归 (Deming Regression)**: 这是一种在自变量和因变量都存在误差时使用的方法。 它通过最小化数据点到回归直线的**正交距离**来估计参数，而不是像 OLS 那样只最小化垂直距离。 这种方法需要一个关键的额外信息：**因变量误差的方差与自变量误差的方差之比** ($\\lambda = \\sigma_\\epsilon^2 / \\sigma_\\delta^2$)。 当这个比率已知时，可以得到一致的估计。\n",
    "\n",
    "*   **正交距离回归 (Orthogonal Distance Regression, ODR)**: 这是戴明回归的一个更广义的形式，可以应用于非线性模型。 其核心思想同样是最小化点到拟合曲线的正交距离。\n",
    "\n",
    "*   **工具变量法 (Instrumental Variables, IV)**: 这是经济学中非常流行的一种方法。 它通过引入一个或多个“工具变量” `Z` 来解决问题。一个有效的工具变量 `Z` 必须满足两个核心条件：\n",
    "    1.  **相关性 (Relevance)**: 工具变量 `Z` 必须与内生的自变量 `X` 相关。\n",
    "    2.  **外生性 (Exogeneity)**: 工具变量 `Z` 只能通过影响 `X` 来影响 `Y`，而不能与因变量的误差项 `ε` 相关。\n",
    "    通过两阶段最小二乘法（2SLS）等方法，IV 能够有效地分离出 `X` 中不受误差项影响的部分，从而得到一致的参数估计。\n",
    "\n",
    "*   **矩量法 (Method of Moments)**: 如果测量误差的方差是已知的，或者可以通过重复测量等方式估计出来，那么可以使用矩量法来修正因测量误差带来的偏误。\n",
    "\n",
    "### 5. 总结\n",
    "\n",
    "| 特征 | 经典回归模型 (OLS) | 误差在变量模型 (EIV) |\n",
    "| :--- | :--- | :--- |\n",
    "| **核心假设** | 只有因变量 Y 有误差，自变量 X 是精确的。 | 因变量 Y 和自变量 X **都**存在测量误差。 |\n",
    "| **目标** | 最小化残差的**垂直**平方和。 | 最小化数据点到回归线的**正交**距离或使用其他修正方法。 |\n",
    "| **当 X 有误差时** | 参数估计**有偏**（通常是衰减偏误）。 | 通过特定方法（如戴明回归、IV）可获得**一致**的估计。 |\n",
    "| **适用场景** | 自变量测量非常精确的受控实验。 | 经济数据分析、医学测量、物理实验等自变量无法精确测量的场景。 |\n",
    "\n",
    "总而言之，EIV 模型是对现实世界数据更精确的描述，它承认了测量的局限性。当有理由相信自变量存在不可忽略的测量误差时，放弃传统的 OLS 回归而选择 EIV 模型（如戴明回归、工具变量法等）是获得更准确、更可靠结论的关键一步。"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "1b376977",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--- 戴明回归 (Deming Regression) 结果 ---\n",
      "估计的截距: 0.7066\n",
      "估计的斜率: 2.0906\n",
      "----------------------------------------\n",
      "--- 普通最小二乘法 (OLS) 结果 ---\n",
      "估计的截距: 1.5283\n",
      "估计的斜率: 1.9232\n",
      "----------------------------------------\n",
      "真实参数: 截距=1.0, 斜率=2.0\n"
     ]
    },
    {
     "data": {
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",
      "text/plain": [
       "<Figure size 1200x800 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.odr import ODR, Model, Data\n",
    "\n",
    "# --- 1. 生成模拟数据 ---\n",
    "# 假设真实的线性关系是 y = 2x + 1\n",
    "true_beta = np.array([1.0, 2.0])  # [截距, 斜率]\n",
    "n_points = 100\n",
    "\n",
    "# 生成真实的、无误差的 x* 值\n",
    "x_true = np.linspace(0, 10, n_points)\n",
    "y_true = true_beta[0] + true_beta[1] * x_true\n",
    "\n",
    "# 为 x 和 y 加上测量误差，生成我们实际观测到的数据\n",
    "# 假设 x 的误差标准差为 0.8，y 的误差标准差为 1.2\n",
    "x_error_std = 0.8\n",
    "y_error_std = 1.2\n",
    "\n",
    "# 使用正态分布生成随机误差\n",
    "x_error = np.random.normal(0, x_error_std, n_points)\n",
    "y_error = np.random.normal(0, y_error_std, n_points)\n",
    "\n",
    "# 观测到的数据 (x_obs, y_obs)\n",
    "x_obs = x_true + x_error\n",
    "y_obs = y_true + y_error\n",
    "\n",
    "# --- 2. 定义线性模型函数 ---\n",
    "# ODR 需要一个函数来定义模型，格式为 f(beta, x)\n",
    "# beta 是一个包含模型参数的列表或数组\n",
    "def linear_func(beta, x):\n",
    "    \"\"\"线性函数 y = b0 + b1*x\"\"\"\n",
    "    return beta[0] + beta[1] * x\n",
    "\n",
    "# --- 3. 执行戴明回归 (Deming Regression) ---\n",
    "# 戴明回归的关键是需要知道 x 和 y 的误差方差之比\n",
    "# variance_ratio = (y_error_std**2) / (x_error_std**2)\n",
    "# 在 scipy.odr 中，我们直接提供误差的标准差 sd_x 和 sd_y\n",
    "# 如果只知道比率 lambda，可以设置 sd_x=1, sd_y=sqrt(lambda)\n",
    "\n",
    "# 创建一个 Model 对象\n",
    "linear_model = Model(linear_func)\n",
    "\n",
    "# 创建一个 Data 对象，包含观测数据和误差标准差\n",
    "# wd 和 we 分别是 x 和 y 误差方差的倒数 (1/std**2)\n",
    "# 如果我们假设所有点的误差方差相同，可以直接提供 sd_x 和 sd_y\n",
    "data = Data(x_obs, y_obs, wd=1./x_error_std**2, we=1./y_error_std**2)\n",
    "\n",
    "\n",
    "# 创建 ODR 对象，并设置初始猜测的参数值\n",
    "odr = ODR(data, linear_model, beta0=[0.5, 1.5]) # beta0 是对 [截距, 斜率] 的初始猜测\n",
    "\n",
    "# 运行 ODR 拟合\n",
    "odr_output = odr.run()\n",
    "\n",
    "# 提取戴明回归的结果\n",
    "beta_deming = odr_output.beta\n",
    "print(\"--- 戴明回归 (Deming Regression) 结果 ---\")\n",
    "print(f\"估计的截距: {beta_deming[0]:.4f}\")\n",
    "print(f\"估计的斜率: {beta_deming[1]:.4f}\")\n",
    "print(\"-\" * 40)\n",
    "\n",
    "# --- 4. 执行普通最小二乘法 (OLS) 作为对比 ---\n",
    "# OLS 可以通过 numpy.polyfit 实现 (一阶多项式)\n",
    "beta_ols = np.polyfit(x_obs, y_obs, 1) # 返回 [斜率, 截距]\n",
    "beta_ols = beta_ols[::-1] # 调整顺序为 [截距, 斜率]\n",
    "\n",
    "print(\"--- 普通最小二乘法 (OLS) 结果 ---\")\n",
    "print(f\"估计的截距: {beta_ols[0]:.4f}\")\n",
    "print(f\"估计的斜率: {beta_ols[1]:.4f}\")\n",
    "print(\"-\" * 40)\n",
    "\n",
    "print(f\"真实参数: 截距={true_beta[0]}, 斜率={true_beta[1]}\")\n",
    "\n",
    "# --- 5. 可视化结果 ---\n",
    "plt.figure(figsize=(12, 8))\n",
    "\n",
    "# 绘制观测数据点\n",
    "plt.scatter(x_obs, y_obs, label='data collected(with bias)', alpha=0.6)\n",
    "\n",
    "# 绘制真实的线性关系\n",
    "plt.plot(x_true, y_true, 'k--', label=f'real relation (y={true_beta[1]}x + {true_beta[0]})', linewidth=2)\n",
    "\n",
    "# 绘制戴明回归拟合线\n",
    "plt.plot(x_true, linear_func(beta_deming, x_true), 'r-', label=f'Deming (K={beta_deming[1]:.2f})', linewidth=2)\n",
    "\n",
    "# 绘制 OLS 拟合线\n",
    "plt.plot(x_true, linear_func(beta_ols, x_true), 'g-.', label=f'OLS (K={beta_ols[1]:.2f})', linewidth=2)\n",
    "\n",
    "plt.title('Deming vs. OLS')\n",
    "plt.xlabel(' X')\n",
    "plt.ylabel(' Y')\n",
    "plt.legend()\n",
    "plt.grid(True)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "231701f3",
   "metadata": {},
   "source": [
    "![](http://cdn.sealight.site/notes/202510151626857.png)\n",
    "\n",
    "这道题的答案是 **B**。\n",
    "\n",
    "一个最简单的线性回归模型是简单线性回归，其数学表达式为：\n",
    "\n",
    "> y = β₀ + β₁x + ε\n",
    "\n",
    "在这个模型中：\n",
    "*   **y** 是因变量（你想要预测的值）。\n",
    "*   **x** 是自变量（用来预测 y 的值）。\n",
    "*   **β₀** 是截距项（intercept），代表当 x=0 时 y 的预测值。它是一个系数。\n",
    "*   **β₁** 是斜率（slope），代表 x 每增加一个单位，y 的平均变化量。它也是一个系数。\n",
    "*   **ε** 是误差项，代表模型无法解释的变异。\n",
    "\n",
    "因此，构建一个最简单的线性回归模型需要 **2个系数**：截距 (β₀) 和斜率 (β₁)。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e42ebec3",
   "metadata": {},
   "source": [
    "# SSE 残差平方和\n",
    "\n",
    "什么是 SSE？\n",
    "SSE (Sum of Squared Errors)，即残差平方和，是统计学和机器学习中衡量模型预测效果的一个重要指标。它的计算方法如下：\n",
    "- 第一步：计算残差 (Error/Residual)\n",
    "残差是指一个数据点的真实值 (Actual Value) 与模型给出的预测值 (Predicted Value) 之间的差异。\n",
    "> 残差 = 真实值 - 预测值\n",
    "\n",
    "第二步：计算残差的平方 (Squared Errors)\n",
    "为了避免正负残差相互抵消，并加大对较大误差的“惩罚”，我们需要将每个残差值进行平方。\n",
    "\n",
    "第三步：求和 (Sum)\n",
    "将所有数据点的残差平方加起来，就得到了 SSE。\n",
    "\n",
    "![](http://cdn.sealight.site/notes/202510151633559.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "e974e359",
   "metadata": {},
   "source": [
    "![](http://cdn.sealight.site/notes/202510151634778.png)\n",
    "\n",
    "这道题的正确答案是 **C**。\n",
    "\n",
    "**1. 理解图表：**\n",
    "\n",
    "*   **横轴 (X-axis)**：代表训练的**迭代次数 (Iterations)**。每一次迭代，模型都会更新一次参数。\n",
    "*   **纵轴 (Y-axis)**：代表模型的**损失函数值 (Loss)** 或代价函数值 (Cost)。这个值衡量了模型当前预测结果与真实标签之间的差距。我们的目标是让这个值尽可能地小。\n",
    "*   **曲线趋势**：图中的损失曲线整体上是**下降**的，这说明模型正在学习，预测越来越准。然而，曲线并不是平滑下降，而是充满了**剧烈的震荡和噪声**。\n",
    "\n",
    "**2. 关键概念：梯度下降的三种方式**\n",
    "\n",
    "为了理解为什么曲线会震荡，我们需要了解梯度下降的三种主要实现方式。梯度下降是神经网络等模型用来最小化损失函数、更新参数的核心算法。\n",
    "\n",
    "*   **批量梯度下降 (Batch Gradient Descent)**\n",
    "    *   **工作方式**：在每一次迭代中，算法会**遍历整个训练数据集**，计算所有样本的平均梯度，然后用这个平均梯度来更新一次模型参数。\n",
    "    *   **Loss 曲线特点**：因为每次更新都考虑了所有数据，所以梯度的方向非常稳定和准确。这会导致损失曲线**非常平滑地下降**，几乎没有震荡。\n",
    "    *   **缺点**：当数据集非常大时，计算成本极高，训练速度很慢。\n",
    "\n",
    "*   **随机梯度下降 (Stochastic Gradient Descent, SGD)**\n",
    "    *   **工作方式**：在每一次迭代中，算法只**随机选择一个样本**来计算梯度，并立即更新参数。\n",
    "    *   **Loss 曲线特点**：由于每次只看一个样本，梯度的方向会充满噪声，非常不稳定。这会导致损失曲线**剧烈震荡**，但总体趋势是下降的。\n",
    "    *   **优点**：训练速度快，计算开销小。震荡有时还能帮助模型跳出局部最优解。\n",
    "\n",
    "*   **小批量梯度下降 (Mini-batch Gradient Descent)**\n",
    "    *   **工作方式**：这是上述两种方法的折中。它在每次迭代中，从整个数据集中随机选择一小批（a mini-batch，比如 32, 64, 128 个样本）数据，计算这批数据的平均梯度来更新参数。\n",
    "    *   **Loss 曲线特点**：相比批量梯度下降，它因为只用了一部分数据，所以曲线会有**一定的震荡**。相比随机梯度下降，它又因为用了一批数据的平均梯度，所以比单个样本更稳定，震荡会**平缓得多**。这是在实践中最常用的方法。\n",
    "\n",
    "**3. 结合图表进行判断**\n",
    "\n",
    "现在我们回头看图中的 Loss 曲线：它**整体下降**，但**震荡非常剧烈**。\n",
    "\n",
    "*   **对比批量梯度下降 (Batch)**：如果是批量梯度下降，曲线应该是平滑的。图中的剧烈震荡表明，这**不可能是**一个正常的批量梯度下降训练过程。如果你的本意是使用批量梯度下降却得到了这样的图，说明训练**可能出了问题**（例如，学习率设置得过高）。\n",
    "\n",
    "*   **对比小批量梯度下降 (Mini-batch)**：如果是小批量梯度下降，曲线有震荡是正常的。图中的震荡虽然存在，但其幅度对于 Mini-batch 来说是**合理且常见**的。每次迭代的 mini-batch 都不同，导致计算出的梯度有差异，从而使 Loss 值上下波动，但只要总体趋势向下，就说明训练在有效进行。\n",
    "\n",
    "**结论：**\n",
    "\n",
    "*   对于 **Mini-batch 梯度下降**，这张图是**合理**的。\n",
    "*   对于 **批量梯度下降**，这张图是不合理的，**可能有问题**。\n",
    "\n",
    "因此，选项 **C** \"如果你正在使用mini-batch梯度下降，那看上去是合理的；而如果你在批量梯度下降，那可能有问题\" 是最准确的描述。\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "126b4640",
   "metadata": {},
   "source": [
    "![](http://cdn.sealight.site/notes/202510151702945.png)\n",
    "A. 均方误差 (Mean Squared Error, MSE)\n",
    "> MSE 计算的是误差的平方。这意味着，如果一个异常点导致了很大的误差（比如预测差了 500 万），这个误差在平方后会变得极其巨大 (500万²)\n",
    "\n",
    "B. 平均绝对误差 (Mean Absolute Error, MAE) \n",
    "> 极端值效果线性增长\n",
    "\n",
    "C. Huber 损失 (Huber Loss)\n",
    "\n",
    "当误差的绝对值小于 δ 时（即预测值与真实值比较接近），它采用平方误差 (类似 MSE) 的计算方式。这使得它在误差较小时像 MSE 一样平滑可导，有利于梯度下降算法的稳定收敛。\n",
    "\n",
    "当误差的绝对值大于 δ 时（即遇到了异常点），它采用线性误差 (类似 MAE) 的计算方式。这使得它在处理大误差时，惩罚不会被过度放大，从而保证了对异常值的鲁棒性。\n",
    "\n",
    "D. 加权均方误差 (Weighted Mean Squared Error, WMSE)\n",
    "\n",
    "虽然 WMSE 可以用来处理异常值，但它有一个前提：你需要事先识别出哪些是异常点并为它们设置权重。在很多情况下，我们无法预先知道所有异常点。相比之下，Huber 损失是一种更通用的、不需要预先识别异常点的解决方案。\n",
    "\n",
    "![](http://cdn.sealight.site/notes/202510151705477.png)"
   ]
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   "id": "282bfcd5",
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   "source": [
    "![](http://cdn.sealight.site/notes/202510151714477.png)\n",
    "![](http://cdn.sealight.site/notes/202510151721741.png)\n",
    "![](http://cdn.sealight.site/notes/202510151741894.png)"
   ]
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   "execution_count": null,
   "id": "12dc1857",
   "metadata": {},
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